Investigates the Drazin inverse of matrix sums, highlighting new applications in block matrices.
In this paper, we investigate additive properties of the Drazin inverse of two matrices. A formula is given for the Drazin inverse of the sum of two matrices P, Q ∈ C^{{n×n}} under the conditions that P² QP = 0, Q² P = 0 and (QP)ᵈ = 0. As an application, we give some new representations for the Drazin inverse of a 2 × 2 block matrix.
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Guo et al. (2025) studied this question.
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